Space of modular forms of level 112, weight 10, and Character 112.i

• Label: 112.10.i
• Level: $112$
• Weight: $10$
• Character orbit: 112.i
• Rep. character: $\chi_{112}(65,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $70$
• Newform subspaces: $6$
• Sturm bound: $160$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 112 = 2^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	112.i (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(160\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(112, [\chi])\).

	Total	New	Old
Modular forms	300	74	226
Cusp forms	276	70	206
Eisenstein series	24	4	20

Trace form

70 * q + 163 * q^3 - q^5 + 1028 * q^7 - 216514 * q^9 - 32929 * q^11 - 4 * q^13 - 39362 * q^15 - q^17 + 1116997 * q^19 + 336765 * q^21 + 2243129 * q^23 - 12490652 * q^25 - 8542418 * q^27 - 3244436 * q^29 + 2267635 * q^31 + 1322729 * q^33 - 14911701 * q^35 - 607389 * q^37 - 38243858 * q^39 - 3633996 * q^41 + 45108824 * q^43 + 10789066 * q^45 - 20682243 * q^47 - 48503994 * q^49 - 328207 * q^51 + 47798215 * q^53 + 32637526 * q^55 - 16628838 * q^57 + 146093691 * q^59 - 55094301 * q^61 - 192027066 * q^63 + 233383286 * q^65 + 24049051 * q^67 - 789519934 * q^69 - 369611936 * q^71 + 169842707 * q^73 + 689822172 * q^75 - 674039311 * q^77 + 467746345 * q^79 - 1485637675 * q^81 - 4108779880 * q^83 + 473215062 * q^85 - 301633082 * q^87 + 15492371 * q^89 + 303787112 * q^91 + 736986565 * q^93 - 2677776009 * q^95 - 922365004 * q^97 + 264949324 * q^99

Decomposition of \(S_{10}^{\mathrm{new}}(112, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
112.10.i.a	$112$	$10$	112.i	7.c	$3$	$6$	$3$	$57.684$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None					14.10.c.b	$2$	$0$	\(0\)	\(-71\)	\(-1085\)	\(6796\)	$2^{6}\cdot 7$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-24-24\beta _{1}+\beta _{2}-\beta _{4})q^{3}+(364\beta _{1}+\cdots)q^{5}+\cdots\)
112.10.i.b	$112$	$10$	112.i	7.c	$3$	$6$	$3$	$57.684$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None					14.10.c.a	$2$	$0$	\(0\)	\(233\)	\(-733\)	\(-5012\)	$2^{6}\cdot 3\cdot 7^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-78\beta _{2}+\beta _{3})q^{3}+(-246+5\beta _{1}+\cdots)q^{5}+\cdots\)
112.10.i.c	$112$	$10$	112.i	7.c	$3$	$10$	$5$	$57.684$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None					7.10.c.a	$2$	$0$	\(0\)	\(-161\)	\(1533\)	\(1036\)	$2^{18}\cdot 3^{3}\cdot 7^{4}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-2^{5}\beta _{2}+\beta _{7})q^{3}+(307-307\beta _{2}+\cdots)q^{5}+\cdots\)
112.10.i.d	$112$	$10$	112.i	7.c	$3$	$12$	$6$	$57.684$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None					28.10.e.a	$2$	$0$	\(0\)	\(0\)	\(-966\)	\(-7696\)	$2^{28}\cdot 3^{4}\cdot 7^{7}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{3}-\beta _{4})q^{3}+(-161+161\beta _{1}+\cdots)q^{5}+\cdots\)
112.10.i.e	$112$	$10$	112.i	7.c	$3$	$18$	$9$	$57.684$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None					56.10.i.b	$2$	$0$	\(0\)	\(71\)	\(449\)	\(1084\)	$2^{64}\cdot 3^{5}\cdot 7^{9}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-8\beta _{1}+\beta _{3})q^{3}+(50+50\beta _{1}-\beta _{5}+\cdots)q^{5}+\cdots\)
112.10.i.f	$112$	$10$	112.i	7.c	$3$	$18$	$9$	$57.684$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None					56.10.i.a	$2$	$0$	\(0\)	\(91\)	\(801\)	\(4820\)	$2^{64}\cdot 3^{9}\cdot 7^{8}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(10+10\beta _{1}+\beta _{2}+\beta _{3})q^{3}+(-89\beta _{1}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{10}^{\mathrm{old}}(112, [\chi])\) into lower level spaces

\( S_{10}^{\mathrm{old}}(112, [\chi]) \simeq \) \(S_{10}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(14, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 2}\)